Assume a continuously compounding dollar interest rate of 5%. If you long a 1-year forward contract on a security with a delivery price K of $55, (a) the security to the future (except interest cost). What should be the current forward price F on the security with 1-year maturity? If the current spot price is $50, there is not other costs or benefits in carrying (b) position in the 1-year forward with a delivery price of $55? Based on your calculated forward price, what is the current value of your long
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- Define the stated (quoted) or nominal rate INOM as well as the periodic rate IPER. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why? What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The discount rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual end-of-year payment to be received from year 24 through year 40Let’s say we have a situation where all 12-month LIBOR forward rates at 8% per annum with annual compounding. All cap volatilities are 16%. Estimate the difference between the way a sophisticated trader and an unsophisticated trader would value a LIBOR-in-arrears swap where payments are made annually and the life of the swap is 5 years and 10 years. Also, assume a notional principal of $1 million and no difference between the risk-free discount rate and LIBOR rates.
- 1. Suppose a financial asset, ABC, is the underlying asset for a futures contract with settlement of 6 months from now. You know the following about this financial asset and futures contract in the cash market ABC is selling for $80; ABC pays $8 per year in two semiannual payments of $4, and the next semiannual payment is due exactly 6 months from now; and the current 6month interest rate at which funds can be loaned or borrowed is 6%. a) Compute for the profit for the transaction? b) What is the theoretical (or equilibrium) futures price? c) What action would you take if the futures price is $837 d) What action would you take if the futures price is $76? SHOW SOLUTIONS PLEASE DONT USE MSEXCELYou are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The nominal interest rate is assumed to be 8%, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (for 17 years)?Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150.
- You attempt to finance a 10-year guaranteed investment contract (GIC). The paymentmade by policyholder is $100 million. Suppose the promised annual interest rate of theGIC is 5%. The bond you want to use is a 15-year, 5% annual coupon rate bond (semiannually paid). Its face value is $100 million and you bought at par. Suppose the newinterest rate in the life of GIC stay constantly at 6%. Answer the following questions:(1). What is the promised payment of the GIC?(2). Calculate the total return of the investment.The real risk-free rate is 3.25%, and inflation is expected to be 3.75% for the next 2 years. A 2-year Treasury security yields 9.25%. What is the maturity risk premium for the 2-year security? Round your answer to two decimal places.you are considering investing in a four year security which pays 6,000 in one year. 6,000 in two years, 6,000 in 3 years and 17,500 in 4 years. the security currently trades at a price of of 18,483.77. What is the yield to maturity of the security? What is duration?
- Assuming away any risk differential of investing in a two-year security for two years or a on-year security followed by another one-year security during year two, we can calculate the one-year interest rate expected by market investors next year For example, if a two-year security offers an annual interest rate of 6% for each of two years and a one-year security offers an annual interest rate of 5%, the one year rate one year from today impounded in the two-year rate must be 7%. In other words, if an investor in a two-year security earns 65 for each of two years, the investor will earn 12% over the two year period -- assuming away the affect of compounding (interest on Interest) Since we are assuming a strategy of investing in a one-year instrument followed by another one-year instrument is equal in risk to investing in a two-year instrument for two years, the average annual return of the two sequential one-year securities must also sum to 12%. Given that a one-year security currently…Suppose you pay 10 to buy a European (K=100, t=2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is 110.You are trying to buy an interest rate swap that will give you floating LIBOR interest for the next 3 years. The notional principal is $100,000 and the settlement is annual. If the annual LIBOR forward rates for the next three years are such that f0,1 = 3%, f1,2 = 3.5% and f2,3 = 4% (fx,y = forward rates between year x and y), determine the fixed rate of this interest rate swap. (Note: Fixed rate in an interest rate swap is a choice variable as in this case. You can buy an interest rate swap as a speculator without having any assets.)